Existence of periodic orbits for piecewise-smooth vector fields with sliding region via Conley theory
| Autor: | Romero, Angie T. S., Vieira, Ewerton R. |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | The Conley theory has a tool to guarantee the existence of periodic trajectories in isolating neighborhoods of semi-dynamical systems. We prove that the positive trajectories generated by a piecewise-smooth vector field $Z=(X, Y)$ defined in a closed manifold of three dimensions without the scape region produces a semi-dynamical system. Thus, we have built a semiflow that allows us to apply the classical Conley theory. Furthermore, we use it to guarantee the existence of periodic orbits in this class of piecewise-smooth vector fields. Comment: 27 pages, 20 figures |
| Databáze: | arXiv |
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